Download or read book Zero Range Potentials and Their Applications in Atomic Physics written by Yu.N. Demkov and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Self Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians written by Matteo Gallone and published by Springer Nature. This book was released on 2023-04-04 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.

Download or read book Theory of Electron Atom Collisions Part One Potential Scattering written by Philip G. Burke and published by Springer Science & Business Media. This book was released on 1995-04-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors aim to hone the theory of electron-atom and electron-ion collisions by developing mathematical equations and comparing their results to the wealth of recent experimental data. This first of three parts focuses on potential scattering, and will serve as an introduction to many of the concepts covered in Parts II and III. As these processes occur in so many of the physical sciences, researchers in astrophysics, atmospheric physics, plasma physics, and laser physics will all benefit from the monograph.

Download or read book Contact Interactions in Quantum Mechanics Theory Mathematical Aspects and Applications written by Manuel Gadella and published by Frontiers Media SA. This book was released on 2021-03-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Supercomputing Collision Processes and Applications written by Kenneth L. Bell and published by Springer Science & Business Media. This book was released on 1999-08-31 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Philip G. Burke, CBE, FRS formally retired on 30 September 1998. To recognise this occasion some of his colleagues, friends, and former students decided to hold a conference in his honour and to present this volume as a dedication to his enormous contribution to the theoretical atomic physics community. The conference and this volume of the invited talks reflect very closely those areas with which he has mostly been asso- ated and his influence internationally on the development of atomic physics coupled with a parallel growth in supercomputing. Phil’s wide range of interests include electron-atom/molecule collisions, scattering of photons and electrons by molecules adsorbed on surfaces, collisions involving oriented and chiral molecules, and the development of non-perturbative methods for studying multiphoton processes. His devel- ment of the theory associated with such processes has enabled important advances to be made in our understanding of the associated physics, the interpretation of experimental data, has been invaluable in application to fusion processes, and the study of astrophysical plasmas (observed by both ground- and space-based telescopes). We therefore offer this volume as our token of affection and respect to Philip G. Burke, with the hope that it may also fill a gap in the literature in these important fields.

Download or read book Ideas and Methods in Quantum and Statistical Physics Volume 2 written by Sergio Albeverio and published by Cambridge University Press. This book was released on 1992-06-26 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of essays by many of the closest co-workers of Raphael Høegh-Krohn.

Download or read book New Directions in Atomic Physics written by C.T. Whelan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have seen some remarkable advances in the understanding of atomic phenomena. It is now possible to isolate atomic systems in traps, measure in coincidence the fragments of collision processes, routinely produce, and study multicharged ions. One can look at bulk matter in such a way that the fundamental atomic character is clearly evident and work has begun to tease out the properties of anti matter. The papers in this book reflect many aspects of modem Atomic Physics. They correspond to the invited talks at a conference dedicated to the study of "New Directions in Atomic Physics," which took place in Magdalene College, Cambridge in July of 1998. The meeting was designed as a way of taking stock of what has been achieved and, it was hoped, as a means of stimulating new research in new areas, along new lines. Consequently, an effort was made to touch on as many directions as we could in the four days of the meeting. We included some talks which overviewed whole subfields, as well as quite a large number of research contributions. There is a unity to Physics and we tried to avoid any artificial division between theory and experiment. We had roughly the same number of talks from those who are primarily concerned with making measurements, and from those who spend their lives trying to develop the theory to describe the experiments.

Download or read book Coherence in Atomic Collision Physics written by H.J. Beyer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last two decades the experimental investigation of atomic coherence phenomena has made rapid progress. Detailed studies have been performed of angular correlations, spin polarization effects, angular momen tum transfer, and the alignment parameters which characterize the charge cloud of excited atoms. The enormous growth in the number of these investigations was made possible through substantial development and application of new experimental technology, the development of sophisti cated theoretical models and numerical methods, and a fine interplay between theory and experiment. This interplay has resulted in a deeper understanding of the physical mechanisms of atomic collision processes. It is the purpose of the chapters in this book to provide introductions for nonspecialists to the various fields of this area as well as to present new experimental and theoretical results and ideas. The interest in spin-dependent interactions in electron-atom scattering has a long history; it dates back to the early investigations of Mott in 1929. While the more traditional measurements in this field were concerned with the determination of spin polarization and asymmetries, the range of investi gations has been expanded enormously during the last few years and now includes many observables sensitive to one or more of the various spin dependent interactions. The understanding of these effects requires a theoretical description of the orientation and alignment parameters of the target atoms, of the forma tion of resonances, of the influence of electron-exchange processes, and of the relativistic interactions inside the atom and between projectile and target.

Download or read book Density Matrix Theory and Applications written by Karl Blum and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary variables. The use of density matrix methods also has the advan tage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incompletely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Download or read book Modern Analysis and Applications written by Vadim Adamyan and published by Springer Science & Business Media. This book was released on 2009-08-29 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

Download or read book Wave propagation Scattering theory written by M. Sh Birman and published by American Mathematical Soc.. This book was released on 1993-12-20 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this collection were written primarily by members of the St. Petersburg seminar in mathematical physics. The seminar, now run by O. A. Ladyzhenskaya, was initiated in 1947 by V. I. Smirnov, to whose memory this volume is dedicated. The papers in the collection are devoted mainly to wave propagation processes, scattering theory, integrability of nonlinear equations, and related problems of spectral theory of differential and integral operators. The book is of interest to mathematicians working in mathematical physics and differential equations, as well as to physicists studying various wave propagation processes.

Download or read book Quantum Dynamics of a Particle in a Tracking Chamber written by Rodolfo Figari and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the original formulation of quantum mechanics the existence of a precise border between a microscopic world, governed by quantum mechanics, and a macroscopic world, described by classical mechanics was assumed. Modern theoretical and experimental physics has moved that border several times, carefully investigating its definition and making available to observation larger and larger quantum systems. The present book examines a paradigmatic case of the transition from quantum to classical behavior: A quantum particle is revealed in a tracking chamber as a trajectory obeying the laws of classical mechanics. The authors provide here a purely quantum-mechanical description of this behavior, thus helping to illuminate the nature of the border between the quantum and the classical.

Download or read book Geometric Methods in Physics XXXVIII written by Piotr Kielanowski and published by Springer Nature. This book was released on 2020-10-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Download or read book Theory of Electron Atom Collisions written by Philip G. Burke and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors aim to hone the theory of electron-atom and electron-ion collisions by developing mathematical equations and comparing their results to the wealth of recent experimental data. This first of three parts focuses on potential scattering, and will serve as an introduction to many of the concepts covered in Parts II and III. As these processes occur in so many of the physical sciences, researchers in astrophysics, atmospheric physics, plasma physics, and laser physics will all benefit from the monograph.

Download or read book Selected Topics on Electron Physics written by D. Murray Campbell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the spring of 1970 Peter Farago organised a three-day conference on Polarised Electron Beams at Carberry Tower, near Edinburgh. Although the development of the gallium arsenide source, which was to revolutionise the world of experimental polarised electron physics, was still some years in the future, the meeting provided an important forum for the exchange of ideas among theoreticians and experimentalists engaged in both high and low energy electron collision studies. As soon as the decision had been taken to hold the 5th European Conference on Atomic and Molecular Physics in Edinburgh in 1995, it occurred to the editors of the present volume that it would be highly appropriate to mark the twenty-fifth anniversary of the Carberry Tower Conference by organising an ECAMP satellite meeting in honour of Peter Farago. The opportunity to pay tribute to Peter's many important contributions in the broad field of electron physics attracted colleagues from allover the world to the symposium, which was held in the rooms of the Royal Society of Edinburgh on 31st March and 1st April 1995. Peter himself, now Professor Emeritus at the University of Edinburgh, was present throughout the meeting. We were particularly happy to welcome back to Edinburgh many participants in the original Carberry Tower conference; these included Professor P. G. Burke, Professor J. Kessler, Professor E. Reichert and Professor H. C. Siegmann, whose review papers had been highlights of the 1970 meeting.

Download or read book Introduction to the Theory of Laser Atom Interactions written by Marvin H. Mittleman and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the explosion of theories and experiments since the appearance of the first edition, the author has revised and expanded his basic text. New sections include up-to-date discussions of multiphoton ionization, and electron-atom and atom-atom scattering in laser fields, reaffirming the work's position as the standard introduction to the field.

Download or read book Advances in Atomic Molecular and Optical Physics written by and published by Academic Press. This book was released on 2011-08-09 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 55 of the Advances in Atomic, Molecular, and Optical Physics Series contains seven contributions, covering a diversity of subject areas in atomic, molecular and optical physics. In their contribution, Stowe, Thorpe, Pe’er, Ye, Stalnaker, Gerginov, and Diddams explore recent developments in direct frequency comb spectroscopy. Precise phase coherence among successive ultrashort pulses of a frequency comb allows one to probe fast dynamics in the time domain and high-resolution structural information in the frequency domain for both atoms and molecules. The authors provide a detailed review of some of the current applications that exploit the unique features of frequency comb spectroscopy and discuss its future directions. Yurvsky, Olshanii and Weiss review theory and experiment of elongated atom traps that confine ultracold gases in a quasi-one-dimensional regime. Under certain conditions, these quasi-one-dimensional gases are well-described by integrable one-dimensional many-body models with exact quantum solutions. Thermodynamic and correlation properties of one such model that has been experimentally realized are reviewed. DePaola, Morgenstein and Andersen discuss magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS), exploring collisions between a projectile and target resulting in charged target fragments. MOTRIMS combines the technology of laser cooling and trapping of target atoms with the momentum analysis of the charged fragments that recoil from the target. The authors review the different MOTRIMS experimental approaches and the spectroscopic and collisional investigations performed so far. Safronova and Johnson give an overview of atomic many-body perturbation theory and discuss why extensions of the theory are needed. They present “all-order results based on a linearized version of coupled cluster expansions and apply the theory to calculations of energies, transition matrix elements and hyperfine constants. Another contribution on atomic theory, authored by Fischer, explores the advantages of expanding the atomic radial wave functions in a B-spline basis. The differential equations are replaced by non-linear systems of equations and the problems of orthogonality requirements can be dealt with using projection operators. Electron-ion collisional processes are analyzed by Mueller, including descriptions of the experimental techniques needed to obtain cross section data and typical values for these cross sections. The present status of the field is discussed in relation to the detailed cross sections and rate coefficients that are needed for understanding laboratory or astrophysical plasmas. Finally, Duan and Monroe review ways to achieve scalable and robust quantum communication, state engineering, and quantum computation. Using radiation and atoms, ions, or atomic ensembles, they show that they can construct scalable quantum networks that are inherently insensitive to noise. Progress in experimental realization of their proposals is outlined. International experts Comprehensive articles New developments